last updated: 2023-08-22
As usual, make sure we have the right packages for this exercise
if (!require("pacman")) install.packages("pacman"); library(pacman)
## Loading required package: pacman
# let's load all of the files we were using and want to have again today
p_load("tidyverse", "knitr", "readr",
"pander", "BiocManager",
"dplyr", "stringr",
"statmod", # required dependency, need to load manually on some macOS versions.
"purrr", # for working with lists (beautify column names)
"reactable") # for pretty tables.
# We also need these Bioconductor packages today.
p_load("edgeR", "AnnotationDbi", "org.Sc.sgd.db")
#NOTE: edgeR loads limma as a dependency
This will be our last differential expression analysis workflow, converting gene counts across samples into meaningful information about genes that appear to be significantly differentially expressed between samples
At the end of this exercise, you should be able to:
library(limma)
library(org.Sc.sgd.db)
# for ease of use, set max number of digits after decimal
options(digits=3)
We saved this file in the last exercise (Read_Counting.Rmd) from the
RSubread package. Now we can load that object back in and assign it to
the variable fc. Be sure to change the file path if you
have saved it in a different location.
path_fc_object <- path.expand("~/Desktop/Genomic_Data_Analysis/Data/yeast_fc_output.Rds")
fc <- readRDS(file = path_fc_object)
If you don’t have that file for any reason, the below code chunk will load a copy of it from Github.
if( !exists("fc") )
{
fc <- read_rds('https://github.com/clstacy/GenomicDataAnalysis_Fa23/raw/main/data/ethanol_stress/yeast_fc_output.Rds')
}
To find the order of files we need, we can get just the part of the column name before the first “.” symbol with this command:
str_split_fixed(fc$counts %>% colnames(), "\\.", n = 2)[, 1]
## [1] "YPS606_MSN24_ETOH_REP1_R1" "YPS606_MSN24_ETOH_REP2_R1"
## [3] "YPS606_MSN24_ETOH_REP3_R1" "YPS606_MSN24_ETOH_REP4_R1"
## [5] "YPS606_MSN24_MOCK_REP1_R1" "YPS606_MSN24_MOCK_REP2_R1"
## [7] "YPS606_MSN24_MOCK_REP3_R1" "YPS606_MSN24_MOCK_REP4_R1"
## [9] "YPS606_WT_ETOH_REP1_R1" "YPS606_WT_ETOH_REP2_R1"
## [11] "YPS606_WT_ETOH_REP3_R1" "YPS606_WT_ETOH_REP4_R1"
## [13] "YPS606_WT_MOCK_REP1_R1" "YPS606_WT_MOCK_REP2_R1"
## [15] "YPS606_WT_MOCK_REP3_R1" "YPS606_WT_MOCK_REP4_R1"
sample_metadata <- tribble(
~Sample, ~Genotype, ~Condition,
"YPS606_MSN24_ETOH_REP1_R1", "msn24dd", "EtOH",
"YPS606_MSN24_ETOH_REP2_R1", "msn24dd", "EtOH",
"YPS606_MSN24_ETOH_REP3_R1", "msn24dd", "EtOH",
"YPS606_MSN24_ETOH_REP4_R1", "msn24dd", "EtOH",
"YPS606_MSN24_MOCK_REP1_R1", "msn24dd", "unstressed",
"YPS606_MSN24_MOCK_REP2_R1", "msn24dd", "unstressed",
"YPS606_MSN24_MOCK_REP3_R1", "msn24dd", "unstressed",
"YPS606_MSN24_MOCK_REP4_R1", "msn24dd", "unstressed",
"YPS606_WT_ETOH_REP1_R1", "WT", "EtOH",
"YPS606_WT_ETOH_REP2_R1", "WT", "EtOH",
"YPS606_WT_ETOH_REP3_R1", "WT", "EtOH",
"YPS606_WT_ETOH_REP4_R1", "WT", "EtOH",
"YPS606_WT_MOCK_REP1_R1", "WT", "unstressed",
"YPS606_WT_MOCK_REP2_R1", "WT", "unstressed",
"YPS606_WT_MOCK_REP3_R1", "WT", "unstressed",
"YPS606_WT_MOCK_REP4_R1", "WT", "unstressed") %>%
# Create a new column that combines the Genotype and Condition value
mutate(Group = factor(
paste(Genotype, Condition, sep = "."),
levels = c(
"WT.unstressed","WT.EtOH",
"msn24dd.unstressed", "msn24dd.EtOH"
)
)) %>%
# make Condition and Genotype a factor (with baseline as first level) for edgeR
mutate(
Genotype = factor(Genotype,
levels = c("WT", "msn24dd")),
Condition = factor(Condition,
levels = c("unstressed", "EtOH"))
)
Now, let’s create a design matrix with this information
group <- sample_metadata$Group
design <- model.matrix(~ 0 + group)
# beautify column names
colnames(design) <- levels(group)
design
## WT.unstressed WT.EtOH msn24dd.unstressed msn24dd.EtOH
## 1 0 0 0 1
## 2 0 0 0 1
## 3 0 0 0 1
## 4 0 0 0 1
## 5 0 0 1 0
## 6 0 0 1 0
## 7 0 0 1 0
## 8 0 0 1 0
## 9 0 1 0 0
## 10 0 1 0 0
## 11 0 1 0 0
## 12 0 1 0 0
## 13 1 0 0 0
## 14 1 0 0 0
## 15 1 0 0 0
## 16 1 0 0 0
## attr(,"assign")
## [1] 1 1 1 1
## attr(,"contrasts")
## attr(,"contrasts")$group
## [1] "contr.treatment"
The count matrix is used to construct a DGEList class object. This is the main data class in the edgeR package. The DGEList object is used to store all the information required to fit a generalized linear model to the data, including library sizes and dispersion estimates as well as counts for each gene.
y <- DGEList(fc$counts, group=group)
colnames(y) <- sample_metadata$Sample
y$samples
## group lib.size norm.factors
## YPS606_MSN24_ETOH_REP1_R1 msn24dd.EtOH 195105 1
## YPS606_MSN24_ETOH_REP2_R1 msn24dd.EtOH 180513 1
## YPS606_MSN24_ETOH_REP3_R1 msn24dd.EtOH 165696 1
## YPS606_MSN24_ETOH_REP4_R1 msn24dd.EtOH 172157 1
## YPS606_MSN24_MOCK_REP1_R1 msn24dd.unstressed 137673 1
## YPS606_MSN24_MOCK_REP2_R1 msn24dd.unstressed 141652 1
## YPS606_MSN24_MOCK_REP3_R1 msn24dd.unstressed 171295 1
## YPS606_MSN24_MOCK_REP4_R1 msn24dd.unstressed 172884 1
## YPS606_WT_ETOH_REP1_R1 WT.EtOH 154719 1
## YPS606_WT_ETOH_REP2_R1 WT.EtOH 169239 1
## YPS606_WT_ETOH_REP3_R1 WT.EtOH 179811 1
## YPS606_WT_ETOH_REP4_R1 WT.EtOH 157740 1
## YPS606_WT_MOCK_REP1_R1 WT.unstressed 186150 1
## YPS606_WT_MOCK_REP2_R1 WT.unstressed 154835 1
## YPS606_WT_MOCK_REP3_R1 WT.unstressed 184436 1
## YPS606_WT_MOCK_REP4_R1 WT.unstressed 172568 1
Human-readable gene symbols can also be added to complement the gene ID for each gene, using the annotation in the org.Sc.sgd.db package.
y$genes <- AnnotationDbi::select(org.Sc.sgd.db,keys=rownames(y),columns="GENENAME")
## 'select()' returned 1:1 mapping between keys and columns
head(y$genes)
## ORF SGD GENENAME
## 1 YDL246C S000002405 SOR2
## 2 YDL243C S000002402 AAD4
## 3 YDR387C S000002795 CIN10
## 4 YDL094C S000002252 <NA>
## 5 YDR438W S000002846 THI74
## 6 YDR523C S000002931 SPS1
Genes with very low counts across all libraries provide little evidence for differential ex- pression. In addition, the pronounced discreteness of these counts interferes with some of the statistical approximations that are used later in the pipeline. These genes should be filtered out prior to further analysis. Here, we will retain a gene only if it is expressed at a count-per-million (CPM) above 60 in at least four samples.
keep <- rowSums(cpm(y) > 60) >= 4
y <- y[keep,]
summary(keep)
## Mode FALSE TRUE
## logical 4518 2609
Where did those cutoff numbers come from?
As a general rule, we don’t want to exclude a gene that is expressed in only one group, so a cutoff number equal to the number of replicates can be a good starting point. For counts, a good threshold can be chosen by identifying the CPM that corresponds to a count of 10, which in this case would be about 60 (due to our fastq files being subsets of the full reads):
cpm(10, mean(y$samples$lib.size))
## [,1]
## [1,] 59.3
Smaller CPM thresholds are usually appropriate for larger libraries.
TMM normalization is performed to eliminate composition biases between libraries. This generates a set of normalization factors, where the product of these factors and the library sizes defines the effective library size. The calcNormFactors function returns the DGEList argument with only the norm.factors changed.
y <- calcNormFactors(y)
y$samples
## group lib.size norm.factors
## YPS606_MSN24_ETOH_REP1_R1 msn24dd.EtOH 195105 1.156
## YPS606_MSN24_ETOH_REP2_R1 msn24dd.EtOH 180513 1.094
## YPS606_MSN24_ETOH_REP3_R1 msn24dd.EtOH 165696 1.074
## YPS606_MSN24_ETOH_REP4_R1 msn24dd.EtOH 172157 0.997
## YPS606_MSN24_MOCK_REP1_R1 msn24dd.unstressed 137673 1.038
## YPS606_MSN24_MOCK_REP2_R1 msn24dd.unstressed 141652 1.046
## YPS606_MSN24_MOCK_REP3_R1 msn24dd.unstressed 171295 0.999
## YPS606_MSN24_MOCK_REP4_R1 msn24dd.unstressed 172884 0.996
## YPS606_WT_ETOH_REP1_R1 WT.EtOH 154719 0.865
## YPS606_WT_ETOH_REP2_R1 WT.EtOH 169239 0.908
## YPS606_WT_ETOH_REP3_R1 WT.EtOH 179811 0.945
## YPS606_WT_ETOH_REP4_R1 WT.EtOH 157740 0.928
## YPS606_WT_MOCK_REP1_R1 WT.unstressed 186150 1.004
## YPS606_WT_MOCK_REP2_R1 WT.unstressed 154835 1.065
## YPS606_WT_MOCK_REP3_R1 WT.unstressed 184436 0.942
## YPS606_WT_MOCK_REP4_R1 WT.unstressed 172568 0.984
The normalization factors multiply to unity across all libraries. A normalization factor below unity indicates that the library size will be scaled down, as there is more suppression (i.e., composition bias) in that library relative to the other libraries. This is also equivalent to scaling the counts upwards in that sample. Conversely, a factor above unity scales up the library size and is equivalent to downscaling the counts. The performance of the TMM normalization procedure can be examined using mean- difference (MD) plots. This visualizes the library size-adjusted log-fold change between two libraries (the difference) against the average log-expression across those libraries (the mean). The below command plots an MD plot, comparing sample 1 against an artificial library constructed from the average of all other samples.
for (sample in 1:nrow(y$samples)) {
plotMD(cpm(y, log=TRUE), column=sample)
abline(h=0, col="red", lty=2, lwd=2)
}
The data can be explored by generating multi-dimensional scaling (MDS) plots. This visualizes the differences between the expression profiles of different samples in two dimensions. The next plot shows the MDS plot for the yeast heatshock data.
points <- c(1,1,2,2)
colors <- rep(c("black", "red"),8)
plotMDS(y, col=colors[group], pch=points[group])
legend("topright", legend=levels(group),
pch=points, col=colors, ncol=2)
This is the first step in a limma analysis that differs from the edgeR workflow.
y <- voom(y, design, plot = T)
# compare this to the edgeR function estimateDisp, which uses a NB distribution.
# y <- estimateDisp(y, design, robust=TRUE)
# plotBCV(y)
What is voom doing?
Counts are transformed to log2 counts per million reads (CPM), where “per million reads” is defined based on the normalization factors we calculated earlier
A linear model is fitted to the log2 CPM for each gene, and the residuals are calculated
A smoothed curve is fitted to the sqrt(residual standard deviation) by average expression (see red line in plot above)
The smoothed curve is used to obtain weights for each gene and sample that are passed into limma along with the log2 CPMs.
Limma uses the lmFit function. This returns a MArrayLM
object containing the weighted least squares estimates for each
gene.
fit <- lmFit(y, design)
head(coef(fit))
## WT.unstressed WT.EtOH msn24dd.unstressed msn24dd.EtOH
## YDR492W 6.77 3.28 6.73 2.76
## YDR508C 9.13 8.59 9.02 9.01
## YDR186C 5.63 6.53 5.78 6.38
## YDR150W 7.77 6.74 7.87 6.57
## YDL182W 8.96 6.63 8.70 7.31
## YDR232W 8.03 7.56 7.68 7.07
# edgeR equivalent
# fit <- glmQLFit(y, design, robust=TRUE)
# head(fit$coefficients)
# plotQLDisp(fit)
Comparisons between groups (log fold-changes) are obtained as contrasts of these fitted linear models:
The final step is to actually test for significant differential
expression in each gene, using the QL F-test. The contrast of interest
can be specified using the makeContrasts function in limma,
the same one that is used by edgeR.
# generate contrasts we are interested in learning about
my.contrasts <- makeContrasts(EtOHvsMOCK.WT = WT.EtOH - WT.unstressed,
EtOHvsMOCK.MSN24dd = msn24dd.EtOH - msn24dd.unstressed,
EtOH.MSN24ddvsWT = msn24dd.EtOH - WT.EtOH,
MOCK.MSN24ddvsWT = msn24dd.unstressed - WT.unstressed,
EtOHvsWT.MSN24ddvsWT = (msn24dd.EtOH-msn24dd.unstressed)-(WT.EtOH-WT.unstressed),
levels=design)
# fit the linear model to these contrasts
res_all <- contrasts.fit(fit, my.contrasts)
# This looks at all of our contrasts in my.contrasts
res_all <- eBayes(res_all)
# eBayes is the alternative to glmQLFTest in edgeR
# This contrast looks at the difference in the stress responses between mutant and WT
# res <- glmQLFTest(fit, contrast = my.contrasts)
top.table <- topTable(res_all, sort.by = "F", n = Inf)
head(top.table, 20)
## ORF SGD GENENAME EtOHvsMOCK.WT EtOHvsMOCK.MSN24dd
## YJL034W YJL034W S000003571 KAR2 3.72 3.299
## YJL052W YJL052W S000003588 TDH1 3.46 2.674
## YGR254W YGR254W S000003486 ENO1 6.11 5.490
## YKL035W YKL035W S000001518 UGP1 4.63 0.616
## YIL053W YIL053W S000001315 GPP1 2.79 3.024
## YJR009C YJR009C S000003769 TDH2 2.39 2.136
## YBR126C YBR126C S000000330 TPS1 5.46 2.547
## YLR249W YLR249W S000004239 YEF3 -2.34 -1.930
## YIL169C YIL169C S000001431 CSS1 -2.20 -2.264
## YCR012W YCR012W S000000605 PGK1 2.17 1.773
## YCL040W YCL040W S000000545 GLK1 8.41 7.900
## YEL071W YEL071W S000000797 DLD3 2.49 3.317
## YGL008C YGL008C S000002976 PMA1 -2.39 -1.989
## YAL005C YAL005C S000000004 SSA1 2.90 1.519
## YCL043C YCL043C S000000548 PDI1 2.22 1.808
## YGL055W YGL055W S000003023 OLE1 -4.28 -3.666
## YMR217W YMR217W S000004830 GUA1 -3.38 -3.296
## YNL209W YNL209W S000005153 SSB2 -2.00 -1.681
## YPL265W YPL265W S000006186 DIP5 2.85 3.155
## YMR011W YMR011W S000004613 HXT2 -4.42 -4.627
## EtOH.MSN24ddvsWT MOCK.MSN24ddvsWT EtOHvsWT.MSN24ddvsWT AveExpr F
## YJL034W -0.2220 0.19435 -0.4164 11.50 1000
## YJL052W -0.8640 -0.07931 -0.7847 12.88 940
## YGR254W -0.7536 -0.13617 -0.6174 11.35 759
## YKL035W -4.0352 -0.02539 -4.0098 9.38 660
## YIL053W -0.0631 -0.29550 0.2324 10.89 539
## YJR009C -0.3295 -0.07751 -0.2520 13.74 528
## YBR126C -3.4203 -0.50803 -2.9123 8.01 429
## YLR249W 0.3379 -0.06984 0.4077 12.43 415
## YIL169C 0.0432 0.10341 -0.0602 12.92 396
## YCR012W -0.4585 -0.06682 -0.3917 13.10 353
## YCL040W -2.0644 -1.55607 -0.5083 7.90 351
## YEL071W 0.6991 -0.12656 0.8257 9.40 338
## YGL008C 0.4125 0.00955 0.4029 12.28 335
## YAL005C -0.9969 0.38262 -1.3795 11.42 329
## YCL043C -0.4555 -0.04622 -0.4093 11.07 310
## YGL055W 0.5466 -0.06327 0.6099 8.79 303
## YMR217W 0.0289 -0.05075 0.0797 9.31 298
## YNL209W 0.2188 -0.09836 0.3171 12.05 297
## YPL265W 0.1944 -0.10685 0.3013 9.12 277
## YMR011W -0.4367 -0.22653 -0.2102 8.73 262
## P.Value adj.P.Val
## YJL034W 5.07e-50 1.32e-46
## YJL052W 2.98e-49 3.89e-46
## YGR254W 1.33e-46 1.15e-43
## YKL035W 6.87e-45 4.48e-42
## YIL053W 2.06e-42 1.08e-39
## YJR009C 3.65e-42 1.59e-39
## YBR126C 1.25e-39 4.67e-37
## YLR249W 3.08e-39 1.00e-36
## YIL169C 1.11e-38 3.20e-36
## YCR012W 2.78e-37 7.25e-35
## YCL040W 3.19e-37 7.56e-35
## YEL071W 9.21e-37 2.00e-34
## YGL008C 1.18e-36 2.37e-34
## YAL005C 1.81e-36 3.38e-34
## YCL043C 9.46e-36 1.65e-33
## YGL055W 1.84e-35 3.00e-33
## YMR217W 2.95e-35 4.29e-33
## YNL209W 2.96e-35 4.29e-33
## YPL265W 2.14e-34 2.94e-32
## YMR011W 9.34e-34 1.22e-31
top.table %>%
tibble() %>%
arrange(adj.P.Val) %>%
mutate(across(where(is.numeric), signif, 3)) %>%
reactable()
## Warning: There was 1 warning in `mutate()`.
## ℹ In argument: `across(where(is.numeric), signif, 3)`.
## Caused by warning:
## ! The `...` argument of `across()` is deprecated as of dplyr 1.1.0.
## Supply arguments directly to `.fns` through an anonymous function instead.
##
## # Previously
## across(a:b, mean, na.rm = TRUE)
##
## # Now
## across(a:b, \(x) mean(x, na.rm = TRUE))
# edgeR equivalent below:
# let's take a quick look at the results
# topTags(res, n=10)
#
# # generate a beautiful table for the pdf/html file.
# topTags(res, n=Inf) %>% data.frame() %>%
# arrange(FDR) %>%
# mutate(logFC=round(logFC,2)) %>%
# mutate(across(where(is.numeric), signif, 3)) %>%
# reactable()
# Let's see how many genes in total are significantly different in any contrast
length(which(top.table$adj.P.Val < 0.05))
## [1] 1895
# let's summarize this and break it down by contrast.
res_all %>%
decideTests(p.value = 0.05, lfc = 0) %>%
summary()
## EtOHvsMOCK.WT EtOHvsMOCK.MSN24dd EtOH.MSN24ddvsWT MOCK.MSN24ddvsWT
## Down 873 850 377 2
## NotSig 866 1016 2004 2606
## Up 870 743 228 1
## EtOHvsWT.MSN24ddvsWT
## Down 164
## NotSig 2328
## Up 117
# Bonus: limma allows us to create a venn diagram of these contrasts
# up & downregulated genes
res_all %>%
decideTests(p.value = 0.05, lfc = 1) %>%
vennDiagram(include=c("up", "down"),
lwd=0.75,
mar=rep(2,4), # increase margine size
counts.col= c("red", "blue"),
show.include=TRUE)
It is interesting to see all of the contrasts simultaneously, but often we may want to look at just a single contrast (and get the corresponding probabilities). Here is how we do that:
# fit the linear model to these contrasts
res <- contrasts.fit(fit, my.contrasts[,"EtOHvsWT.MSN24ddvsWT"])
# This contrast looks at the difference in the stress responses between mutant and WT
res <- eBayes(res)
# Note that there is no longer an "F" column, because we only look at one contrast.
top.table <- topTable(res, sort.by = "P", n = Inf)
head(top.table, 20)
## ORF SGD GENENAME logFC AveExpr t P.Value adj.P.Val
## YKL035W YKL035W S000001518 UGP1 -4.010 9.38 -19.98 9.76e-28 2.55e-24
## YPR149W YPR149W S000006353 NCE102 -3.857 7.58 -10.73 2.01e-15 2.63e-12
## YPL004C YPL004C S000005925 LSP1 -2.665 8.35 -10.59 3.36e-15 2.92e-12
## YDR343C YDR343C S000002751 HXT6 -5.274 7.30 -10.00 3.03e-14 1.87e-11
## YML100W YML100W S000004566 TSL1 -7.795 6.02 -9.95 3.59e-14 1.87e-11
## YDR077W YDR077W S000002484 SED1 -1.474 10.79 -9.79 6.42e-14 2.79e-11
## YMR105C YMR105C S000004711 PGM2 -6.545 6.22 -9.22 5.63e-13 1.82e-10
## YAL005C YAL005C S000000004 SSA1 -1.380 11.42 -9.19 6.21e-13 1.82e-10
## YKL150W YKL150W S000001633 MCR1 -3.068 7.77 -9.19 6.29e-13 1.82e-10
## YGR086C YGR086C S000003318 PIL1 -1.671 8.89 -8.78 2.94e-12 7.67e-10
## YBR126C YBR126C S000000330 TPS1 -2.912 8.01 -8.56 6.79e-12 1.61e-09
## YOL155C YOL155C S000005515 HPF1 -1.526 10.24 -8.52 7.95e-12 1.73e-09
## YJR045C YJR045C S000003806 SSC1 -1.243 10.38 -8.30 1.88e-11 3.77e-09
## YLL024C YLL024C S000003947 SSA2 -0.959 12.91 -7.81 1.22e-10 2.28e-08
## YDR133C YDR133C S000002540 <NA> -1.602 8.76 -7.72 1.77e-10 3.08e-08
## YFR053C YFR053C S000001949 HXK1 -7.158 4.54 -7.58 3.05e-10 4.98e-08
## YFL014W YFL014W S000001880 HSP12 -7.320 3.77 -7.41 5.94e-10 9.12e-08
## YMR196W YMR196W S000004809 <NA> -5.471 5.75 -7.37 6.84e-10 9.57e-08
## YJL078C YJL078C S000003614 PRY3 -1.674 8.90 -7.37 6.97e-10 9.57e-08
## YMR261C YMR261C S000004874 TPS3 -2.370 7.45 -7.35 7.35e-10 9.59e-08
## B
## YKL035W 52.6
## YPR149W 24.6
## YPL004C 24.3
## YDR343C 21.6
## YML100W 19.5
## YDR077W 21.2
## YMR105C 17.7
## YAL005C 18.9
## YKL150W 19.2
## YGR086C 17.6
## YBR126C 16.8
## YOL155C 16.5
## YJR045C 15.6
## YLL024C 13.5
## YDR133C 13.6
## YFR053C 11.1
## YFL014W 10.5
## YMR196W 11.4
## YJL078C 12.2
## YMR261C 12.3
top.table %>%
tibble() %>%
arrange(adj.P.Val) %>%
mutate(across(where(is.numeric), signif, 3)) %>%
reactable()
We need to make sure and save our output file(s).
# Choose topTags destination
dir_output_limma <-
path.expand("~/Desktop/Genomic_Data_Analysis/Analysis/limma/")
if (!dir.exists(dir_output_limma)) {
dir.create(dir_output_limma, recursive = TRUE)
}
# for shairng with others, the topTags output is convenient.
top.table %>% tibble() %>%
arrange(desc(adj.P.Val)) %>%
mutate(adj.P.Val = round(adj.P.Val, 2)) %>%
mutate(across(where(is.numeric), signif, 3)) %>%
write_tsv(., file = paste0(dir_output_limma, "yeast_topTags_limma.tsv"))
# for subsequent analysis, let's save the res object as an R data object.
saveRDS(object = res, file = paste0(dir_output_limma, "yeast_res_limma.Rds"))
Be sure to knit this file into a pdf or html file once you’re finished.
System information for reproducibility:
pander::pander(sessionInfo())
R version 4.2.2 (2022-10-31)
Platform: aarch64-apple-darwin20 (64-bit)
locale: en_US.UTF-8||en_US.UTF-8||en_US.UTF-8||C||en_US.UTF-8||en_US.UTF-8
attached base packages: stats4, stats, graphics, grDevices, utils, datasets, methods and base
other attached packages: org.Sc.sgd.db(v.3.16.0), AnnotationDbi(v.1.60.2), IRanges(v.2.32.0), S4Vectors(v.0.36.2), Biobase(v.2.58.0), BiocGenerics(v.0.44.0), edgeR(v.3.40.2), limma(v.3.54.2), reactable(v.0.4.4), statmod(v.1.5.0), BiocManager(v.1.30.21.1), pander(v.0.6.5), knitr(v.1.43), lubridate(v.1.9.2), forcats(v.1.0.0), stringr(v.1.5.0), dplyr(v.1.1.2), purrr(v.1.0.1), readr(v.2.1.4), tidyr(v.1.3.0), tibble(v.3.2.1), ggplot2(v.3.4.2), tidyverse(v.2.0.0) and pacman(v.0.5.1)
loaded via a namespace (and not attached): httr(v.1.4.6), sass(v.0.4.7), vroom(v.1.6.3), bit64(v.4.0.5), jsonlite(v.1.8.7), bslib(v.0.5.0), highr(v.0.10), blob(v.1.2.4), GenomeInfoDbData(v.1.2.9), yaml(v.2.3.7), pillar(v.1.9.0), RSQLite(v.2.3.1), lattice(v.0.21-8), glue(v.1.6.2), digest(v.0.6.33), XVector(v.0.38.0), colorspace(v.2.1-0), htmltools(v.0.5.5), reactR(v.0.4.4), pkgconfig(v.2.0.3), zlibbioc(v.1.44.0), scales(v.1.2.1), tzdb(v.0.4.0), timechange(v.0.2.0), KEGGREST(v.1.38.0), generics(v.0.1.3), ellipsis(v.0.3.2), cachem(v.1.0.8), withr(v.2.5.0), cli(v.3.6.1), magrittr(v.2.0.3), crayon(v.1.5.2), memoise(v.2.0.1), evaluate(v.0.21), fansi(v.1.0.4), tools(v.4.2.2), hms(v.1.1.3), lifecycle(v.1.0.3), munsell(v.0.5.0), locfit(v.1.5-9.8), Biostrings(v.2.66.0), compiler(v.4.2.2), jquerylib(v.0.1.4), GenomeInfoDb(v.1.34.9), rlang(v.1.1.1), grid(v.4.2.2), RCurl(v.1.98-1.12), rstudioapi(v.0.15.0), htmlwidgets(v.1.6.2), crosstalk(v.1.2.0), bitops(v.1.0-7), rmarkdown(v.2.23), gtable(v.0.3.3), DBI(v.1.1.3), R6(v.2.5.1), fastmap(v.1.1.1), bit(v.4.0.5), utf8(v.1.2.3), stringi(v.1.7.12), parallel(v.4.2.2), Rcpp(v.1.0.11), vctrs(v.0.6.3), png(v.0.1-8), tidyselect(v.1.2.0) and xfun(v.0.39)